Strategies Based On Threats

Ling Zhao

University of Alberta

March 10, 2003

Comparative evaluation of strategies based on the values of direct threats by Tristan Cazenave in Board Games in Academia V, Barcelona, 2002.

Outline

Motivations Direct threats Thermograph Threat strategies Experimental results

Motivations

Apply combinatorial game theory to Go

- independent subgames

- approach the best stategy

Direct threats

Each subgame has at most two moves

Root of the tree

Black: 22 points

White: 15 points

Value: 7 points for black

Sequence after two black moves

Black: 25 points

White: 14 points

Value: 11 points for black

Direct threat: 4 values

A, B, C, D with A >= B >= C >= D

Denoted as (A, B, C, D)

After one black move

=> (A,B)

After one white move

=> (C,D)

Problem model

Given a set of independent subgames with direct threats, how to compute good moves fast and accurately.

(A1,B1,C1,D1)

(A2,B2,C2,D2)

. . .

(An, Bn, Cn, Dn)

Choose which subgame to play a move?

Thermograph

Temperature: 6.5 Mean value: -4.5

Thermograph for direct threat (4,0,-6,-16)

Strategies

Optimal stategy: brute force (NP-hard?) BMove: compare the best Left move

(A,B,C,D) => value B

(A,B) => value A MaxMove:

(A,B,C,D) => value B-C

(A,B) => value A-B

Stategies

Sente Strategy A – B > MaxV => Sente C – D > MaxV => Reverse Sente Sente or Reverse Sente => MaxV *= 2 both => MaxV *= 4 SenteQ Strategy Always choose sente or reverse sente moves

first. Use MaxV to break ties.

MaxThreat stategy

Stategies

HotStrat: compare temperature ThermoStrat: adding all the thermographs of all

the subgame to choose the best subgame to play in.

Experimental results

Randomly choose 5 subgames (A>=B>=C>=D) 8 Strategies playing against each other (56

games one round) 100 rounds

Conclusions

Simple strategy is good enough! Hotstrat strategy is easy to implement and can

get 12% improvement.

Problems (my thoughts) Impact of imprecise evaluation? How to generalize to more than 2 plies?